feat(CategoryTheory): the retract argument

[joelriou]

In a category, if i ≫ p = f, and f has the left lifting property with respect to p, then f is a retract of i. This statement and its dual are formalised, as well as consequences for classes of morphisms which satisfy HasFactorization W₁ W₂. This is applied to classes of morphisms in model categories in #20210.

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[github-actions]

PR summary bf3215b9de

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference
Mathlib.CategoryTheory.MorphismProperty.LiftingProperty	1
Mathlib.CategoryTheory.MorphismProperty.RetractArgument (new file)	595

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Declarations diff

+ RetractArrow.ofLeftLiftingProperty
+ RetractArrow.ofRightLiftingProperty
+ gc_llp_rlp
+ instance (P₁ P₂ : MorphismProperty C)
+ le_llp_iff_le_rlp
+ llp_eq_of_le_llp_of_hasFactorization_of_isStableUnderRetracts
+ llp_of_isIso
+ mem_trivialCofibrations_iff
+ mem_trivialFibrations_iff
+ rlp_eq_of_le_rlp_of_hasFactorization_of_isStableUnderRetracts
+ rlp_of_isIso

You can run this locally as follows

## summary with just the declaration names:
./scripts/declarations_diff.sh <optional_commit>

## more verbose report:
./scripts/declarations_diff.sh long <optional_commit>

The doc-module for script/declarations_diff.sh contains some details about this script.

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No changes to technical debt.

You can run this locally as

./scripts/technical-debt-metrics.sh pr_summary

• The relative value is the weighted sum of the differences with weight given by the inverse of the current value of the statistic.
• The absolute value is the relative value divided by the total sum of the inverses of the current values (i.e. the weighted average of the differences).